2014/09/06 by Leonardo Aguirre, Giovanni Felder, Aguirre, Leonardo +4 · 2 citations
Mathematics · Physics and Astronomy · #14H70 #14N20 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Primary 81R12 #Secondary 20F55 #math-ph #math.MP #msc:14H70 #msc:14N20 #msc:20F55 #msc:81R12
paper · pdf · doi:10.48550/arxiv.1409.2052
13 pages, 2 figures; added detailed description of the B_2 and B_3 cases in the new version
openalex publication_date 2014/09/06 · arxiv created 2015/01/05 · arxiv updated 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini-Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes.